Finite Element Simulation of Axisymmetric Elastic and Electroelastic Wave Propagation Using Local-Domain Wave Packet Enrichment

A local-domain wave packet enriched multiphysics finite element (FE) formulation is employed for accurately solving axisymmetric wave propagation problems in elastic and piezoelastic media, involving complex wave modes and sharp jumps at the wavefronts, which pose challenges to the conventional FE solutions. The conventional Lagrangian interpolations for the displacement and electric potential fields are enriched with the element-domain sinusoidal functions that satisfy the partition of unity condition. The extended Hamilton’s principle is employed to derive the coupled system of equations of motion which is solved using the simple Newmark-$β$ direct time integration scheme without resorting to any remeshing near the wavefronts or post-processing. The performance of the enrichment is assessed for the axisymmetric problems of impact waves in elastic and piezoelectric cylinders and elastic half-space, bulk and Rayleigh waves in the semi-infinite elastic domain and ultrasonic Lamb wave actuation and propagation in plate-piezoelectric transducer system. The element shows significant improvement in the computational efficiency and accuracy over the conventional FE for all problems, including those involving multiple complex wave modes and sharp discontinuities in the fields at the wavefronts.